本书系统阐述模糊逻辑标准完备性证明的各种方法和理论，为初学者尽可能多的提供理论和技术上的细节，使其能尽快进入这一课题的研究工作。特别地，较为详细的介绍了作者在这些方面所做的工作，对IUL完备性的证明进行了详细的论述，并针对主算法的最困难部分给出了实例,这在一般地论文写作是不可能的。

Preface
Chapter 1 Introduction
1.1 Overview of the standard completeness for fuzzy logics
1.2 Standard completeness of IUL
1.3 My work on the standard completeness for IUL and reviewers' comments on it
1.3.1 Reviewers' comments in 2015 by APAL
1.3.2 Reviewers' comments in 2016 by FSS
1.3.3 Reviewers' comments in 2018 by FSS
1.3.4 Reviewers' comments in 2018 on my second paper by JSL
1.3.5 Communication with editors and colleagues
Chapter 2 The Logic HpsUL* and Its Chain Completeness
2.1 The logic HpsUL*
2.2 Proof by cases property and prelinearity property of HpsUL
2.3 The chain completeness for HpsUL
2.4 Extensions of HpsUL
Chapter 3 Jenei and Montagna's Algebraic Method
3.1 The logic MTL and MTL-algebras
3.2 Standard completeness for MTL
3.3 Standard completeness for IMTL
Chapter 4 Wang's Constructions on HpsUL*-Chains
4.1 New extensions of HpsUL* and new algebras
4.2 Structures X on HpsUL*-chains
4.3 Standard completeness for CnIUL and IULω
4.4 A proof of associativity of in X for IUL
Chapter 5 Metcalfe and Montagna's Proof-Theoretic Method
5.1 Standard completeness and the density rule
5.2 Hypersequent calculi
5.3 Cut-elimination
5.4 Density elimination
Chapter 6 Wang's Proof-Theoretic Method
6.1 Introduction
6.2 Proof of the Main theorem: A computational example
6.3 Preprocessing of proof tree
6.4 The generalized density rule (D) for GLΩ
6.5 Extraction of elimination rules
Chapter 7 Standard Completeness for IUL
7.1 Separation of one branch
7.2 Separation algorithm of multiple branches
7.3 The proof of Main theorem
7.4 Final remarks and open problems
Chapter 8 An Extension of Wang's Proof-Theoretic Method
8.1 Introduction
8.2 GpsUL** and its cut-elimination
8.3 GpsULΩ and its generalized density rule (D))
8.4 Density elimination for GpsUL
Chapter 9 Two Big Examples for Separation Algorithms
9.1 Proof of Theorem 7.2.2: A big example
9.1.1 Preprocessing of proof tree τ
9.1.2 Elimination rules
9.1.3 Separation of one branch
9.1.4 Separations of two branches
9.1.5 A concise algorithm
9.1.6 Separation of four branches
9.2 Proof of Lemma 8.4.7: A big example
9.2.1 Maximal nodes, complete sets and their heights
9.2.2 Some copies of G□(特殊公式) can't be contracted in G1(J)
9.2.3 Illustration of Lemma 8.4.7: Construct τ1,2
9.2.4 Remark on construction of T1, (Tij*)
9.2.5 Constructing of τ1,2,3,4
9.2.6 T1，3 is undefined and can't be constructed by the new main algorithm
Bibliography